Back Desimale graad Afrikaans غراد Arabic Grau centesimal AST Град (ъгъл) Bulgarian Grau centesimal Catalan Grad Czech Nygrad Danish Gon German Βαθμός (γεωμετρία) Greek Graduso Esperanto

Gradian

"Grade (angle)" redirects here. For the grade of an inclined surface, see Grade (slope).
"Gon (angle)" redirects here. For n-gon, see Regular polygon.
Not to be confused with Gradient.
gon
Compass graded with 400 gon
General information
Unit ofAngle
Symbolgon, ᵍ, grad
Conversions
1 gon in ...... is equal to ...
   turns   ⁠1/400⁠ turn
   radians   ⁠π/200⁠ rad
≈ 0.0157... rad
   milliradians   5π mrad
≈ 15.71... mrad
   degrees   ⁠9/10⁠°
   minutes of arc   54′

In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) 'angle'), grad, or grade[1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.[2][3][4] It is equivalent to ⁠1/400⁠ of a turn,[5] ⁠9/10⁠ of a degree, or ⁠π/200⁠ of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement, initiated as part of metrication and decimalisation efforts.[6][7][8][Note 1]

In continental Europe, the French word centigrade, also known as centesimal minute of arc, was in use for one hundredth of a grade; similarly, the centesimal second of arc was defined as one hundredth of a centesimal arc-minute, analogous to decimal time and the sexagesimal minutes and seconds of arc.[12] The chance of confusion was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.[13][14]

Gradians are principally used in surveying (especially in Europe),[15][7][16] and to a lesser extent in mining[17] and geology.[18][19]

The gon is officially a legal unit of measurement in the European Union[20]: 9  and in Switzerland.[21] However, the gradian is not part of the International System of Units (SI).[22][20]: 9–10 

  1. ^ Weisstein, Eric W. "Gradian". mathworld.wolfram.com. Retrieved 2020-08-31.
  2. ^ Harris, J. W.; Stocker, H. (1998). Handbook of Mathematics and Computational Science. New York: Springer-Verlag. p. 63.
  3. ^ "NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity or field of science". nist.gov. NIST. Archived from the original on 2017-04-17.
  4. ^ Patrick Bouron (2005). Cartographie: Lecture de Carte (PDF). Institut Géographique National. p. 12. Archived from the original (PDF) on 2010-04-15. Retrieved 2011-07-07.
  5. ^ "Gradian". Art of Problem Solving. Retrieved 2020-08-31.
  6. ^ Balzer, Fritz (1946). Five Place Natural Sine and Tangent Functions in the Centesimal System. Army Map Service, Corps of Engineers, U.S. Army.
  7. ^ a b Zimmerman, Edward G. (1995). "6. Angle Measurement: Transits and Theodolites". In Minnick, Roy; Brinker, Russell Charles (eds.). The surveying handbook (2nd ed.). Chapman & Hall. ISBN 041298511X.
  8. ^ Gorini, Catherine A. (2003). The Facts on File Geometry Handbook. Infobase Publishing. p. 22. ISBN 978-1-4381-0957-2.
  9. ^ Cajori, Florian (1899). A History of Physics in Its Elementary Branches: Including the Evolution of Physical Laboratories. Macmillan. ISBN 9781548494957. The angle through which the torsion-head must be deflected was measured in centesimal divisions of the circle
  10. ^ Ohm, Georg Simon (1826). "Bestimmung des Gesetzes, nach welchem Metalle die Contactelektricität leiten, nebst einem Entwurfe zur Theorie des Voltaischen Apparates und des Schweiggerschen Multiplikators" (PDF). Journal für Chemie und Physik. 46: 137–166. Archived from the original (PDF) on 23 May 2020. German: wurde die Größe der Drehung oben an der Drehwage in Hunderttheilen einer ganzen Umdrehung abgelesen (p. 147) [the amount of rotation at the top of the torsion balance was read in hundred parts of an entire revolution]
  11. ^ Keithley, Joseph F. (1999). The Story of Electrical and Magnetic Measurements: From 500 BC to the 1940s. John Wiley & Sons. ISBN 978-0-7803-1193-0. It hung on a ribbon torsion element with a knob on top, graduated in 100 parts.
  12. ^ Klein, H.A. (2012). The Science of Measurement: A Historical Survey. Dover Books on Mathematics. Dover Publications. p. 114. ISBN 978-0-486-14497-9. Retrieved 2022-01-02.
  13. ^ Frasier, E. Lewis (February 1974), "Improving an imperfect metric system", Bulletin of the Atomic Scientists, 30 (2): 9–44, Bibcode:1974BuAtS..30b...9F, doi:10.1080/00963402.1974.11458078. On p. 42 Frasier argues for using grads instead of radians as a standard unit of angle, but for renaming grads to "radials" instead of renaming the temperature scale.
  14. ^ Mahaffey, Charles T. (1976), "Metrication problems in the construction codes and standards sector", Final Report National Bureau of Standards, NBS Technical Note 915, U.S. Department of Commerce, National Bureau of Commerce, Institute for Applied Technology, Center for Building Technology, Bibcode:1976nbs..reptU....M, The term "Celsius" was adopted instead of the more familiar "centigrade" because in France the word centigrade has customarily been applied to angles.
  15. ^ Kahmen, Heribert; Faig, Wolfgang (2012). Surveying. De Gruyter. ISBN 9783110845716.
  16. ^ Schofield, Wilfred (2001). Engineering surveying: theory and examination problems for students (5th ed.). Butterworth-Heinemann. ISBN 9780750649872.
  17. ^ Sroka, Anton (2006). "Contribution to the prediction of ground surface movements caused by a rising water level in a flooded mine". In Sobczyk, Eugeniusz; Kicki, Jerzy (eds.). International Mining Forum 2006, New Technological Solutions in Underground Mining: Proceedings of the 7th International Mining Forum, Cracow - Szczyrk - Wieliczka, Poland, February 2006. CRC Press. ISBN 9780415889391.
  18. ^ Gunzburger, Yann; Merrien-Soukatchoff, Véronique; Senfaute, Gloria; Piguet, Jack-Pierre; Guglielmi, Yves (2004). "Field investigations, monitoring and modeling in the identification of rock fall causes". In Lacerda, W.; Ehrlich, Mauricio; Fontoura, S. A. B.; Sayão, A. S. F. (eds.). Landslides: Evaluation & Stabilization/Glissement de Terrain: Evaluation et Stabilisation, Set of 2 Volumes: Proceedings of the Ninth International Symposium on Landslides, June 28 -July 2, 2004 Rio de Janeiro, Brazil. Vol. 1. CRC Press. ISBN 978-1-4822-6288-9.
  19. ^ Schmidt, Dietmar; Kühn, Friedrich (2007). "3. Remote sensing: 3.1 Aerial Photography". In Knödel, Klaus; Lange, Gerhard; Voigt, Hans-Jürgen (eds.). Environmental Geology: Handbook of Field Methods and Case Studies. Springer Science & Business Media. ISBN 978-3-540-74671-3.
  20. ^ a b "Directive 80/181/EEC". 27 May 2009. Archived from the original on 22 May 2020. On the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC.
  21. ^ "941.202 Einheitenverordnung" (in German). Archived from the original on 22 May 2020.
  22. ^ Cite error: The named reference SI Brochure 9th ed was invoked but never defined (see the help page).


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